Polymer dynamics in thin p-type conducting films
investigated by ac-electrogravimetry. Kinetics aspects
on anion exclusion, free solvent transfer, and
conformational changes in poly(o-toluidine)
Jeronimo Agrisuelas, Claude Gabrielli, J.J. Garcı́a-Jareño, Hubert Perrot,
Ozlëm Sel, F. Vicente
To cite this version:
Jeronimo Agrisuelas, Claude Gabrielli, J.J. Garcı́a-Jareño, Hubert Perrot, Ozlëm Sel,
et al..
Polymer dynamics in thin p-type conducting films investigated by acelectrogravimetry. Kinetics aspects on anion exclusion, free solvent transfer, and conformational changes in poly(o-toluidine). Electrochimica Acta, Elsevier, 2015, 153, pp.33-43.
<10.1016/j.electacta.2014.11.159>. <hal-01110553>
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Polymer dynamics in thin p-type conducting films investigated by acelectrogravimetry. Kinetics aspects on anion exclusion, free solvent transfer, and
conformational changes in poly(o-toluidine).
J. Agrisuelas*,1, C. Gabrielli2,3, J. J. García-Jareño1, H. Perrot2,3, O. Sel2,3 and F.
Vicente1
1
Departament de Química Física, Universitat de València. C/ Dr. Moliner, 50, 46100,
Burjassot, València, Spain.
2
Sorbonne Universités, UPMC Univ Paris 06, UMR 8235, Laboratoire Interfaces et
Systèmes Electrochimiques, F-75005, Paris, France.
3
CNRS, UMR 8235, LISE, F-75005, Paris, France.
*E-mail: jeronimo.agrisuelas@uv.es
1
Abstract
A new transfer model is proposed to explain ac-electrogravimetry response of pdoped films. This model takes into account the exclusion effect occurring as a result of
the anion transfer. The insertion/expulsion of anions inside a film involves simultaneously
the expulsion/insertion of free solvent molecules. The number of solvent molecules
excluded depends on the volume of anion transferred. Solvent transfer stimulated by the
conformational changes of films constitutes the remaining electrogravimetric response
when the exclusion process cannot explain by itself this response. Consequently, the
kinetics of this free solvent transfer can be directly related to the kinetics of
conformational changes. This model was validated in poly(o-toluidine) thin films where
electrochemical kinetics were quantitatively investigated as a function of the applied
potential. As far as we know, for the first time, charge transfer and conformational
changes could be kinetically separated. This new transfer model may respond to
fundamental questions on the electrochemistry of conducting polymers, which may have
a significant impact on a large number of applications.
Keywords:
Intrinsically
microbalance,
conducting
Electrochemical
polymer,
impedance
Electrochemical
spectroscopy,
quartz
crystal
ac-Electrogravimetry,
Conformational changes.
2
1. Introduction
In order to convert conceptual and experimental findings to practical and relevant
technological devices based on intrinsically conducting polymers (ICPs), several
parameters should be optimized (molecular structure or solvent-electrolyte medium
among others)[1,2]. The conduction mechanism and the electrolyte as a counter ion
source have received substantial attention[3,4]. Inevitably, ICPs immersed in aqueous or
non-aqueous solutions entail the transfer of solvent molecules in permselective
conditions. This aspect is taken into account either qualitatively or quantitatively but the
studies are commonly restricted to overall electrochemical process. Specially, Hillman
and coworkers have extensively studied the mobile species transfer processes with the
intention of achieving a deeper understanding on the redox dynamics of ICPs (spatial
distributions, viscoelasticity, solvent effect, mechanisms)[5–10].
Solvent inside the films acts as a plasticizer, lubricating the inter-molecular
motions and relaxing the film. The inner solvent matrix of a polymeric film can be divided
in two kinds of populations: molecules intimately bound to polymeric structure and free
molecules. The amount of free molecules changes during the charge/discharge process of
the polymer by the transfer between the polymer and solution. The extent of solvent
transfer depends on the solution composition and it does not require to have integer
stoichiometry coefficients[5]. The influence of solvent transfer requires a good
understanding and quantification in technological applications where the polymer film is
in contact with a liquid phase. For example, the driven volume variation in biomimetic
gel motors depends on the number of counterions and solvent molecules exchanged
during the electrochemical reactions[11].
Solvent transfer can be due to different electrochemical-driving forces in
ICPs[5,12,13]: i) Donnan equilibrium to maintain equal chemical potentials inside and
outside of the film, ii) changes of the volume in the hydration matrix inside the film owing
to ion movements or iii) changes in the macromolecular structure of the reactive polymer,
conformational motions. Although there is no a priori relationship with the injected
charge and the non-charged molecules, neutral solvent transfer can be expected to be
controlled by a non-ideal thermodynamic behavior (non-linear film solvation with charge
state)[14,15]. As an example, this control can take place in films where slower electronic
transfer along dynamic chains introduces a slow conformational change with slow noncharged species transfer. However, under specific experimental conditions or for very
3
thin films, the transfer of neutral solvent can be kinetically controlled (although
“indirectly”) because both insertion/expulsion of ions and movements of polymeric
backbones (both kinetically controlled) have a “direct” effect on the solvent
transfer[16,17]. In the view of that, the transfer of neutral solvent, or in other words, the
hydration extent of ICPs could be modulated varying the oxidation state via an external
potential.
The main difficulty in the study of solvent transfers during electrochemical
reaction in ICPs is the neutral character of these molecules. For these reasons,
complementary techniques should be used together with electrochemical techniques like
quartz crystal microbalance to detect mass changes in the polymeric film or probe beam
deflection to detect concentration gradients of species transfer close to the
polymer|solution interface[18–21].
In this paper, ac-electrogravimetry is used to characterize ions and solvent transfer
in the polymer|solution interface. This technique was clearly proven to be helpful in
polymer studies as an easy and fast identification methodology for cation and anion
transfers involved in the charge compensation process together with a noticeable kinetic
information when electrochemical and mass impedance spectroscopy are discussed
together[22–26]. To separate among anion, cation and solvent contributions from the
global electrogravimetric response, it is necessary to find experimental conditions where
the time constants of these three transfers are fairly different[27]. Experimentally, this
situation is not always achieved, especially in complex electroactive systems.
A different strategy is to find an appropriate model and procedure for analyzing
the experimental results. If that is found, isolated kinetic studies of solvent transfer can
be
performed
by
ac-electrogravimetry.
As
a
first
approximation,
partial
electrogravimetric responses can be mathematically obtained from the global response.
An anion-solvent transfer can be analyzed if the cation contribution is eliminated. In a
similar manner, if the anion contribution is eliminated, a partial cation-solvent transfer
can be obtained[27,28]. Recently, the electrogravimetric response of the global free
solvent transfer was separated from the electrogravimetric response of ions
transfer[16,17].
Now, a refined procedure for the interpretation of ac-electrogravimetry results is
proposed to study the anion p-doping of ICPs. Here, the anion exclusion effect is taken
into account[12,29,30]. The anion insertion during the charge balance excludes a specific
4
number of solvent molecules equivalent to the anion volume, which are expelled from the
film during the oxidation. During the reduction, the free volume liberated by anions is
rapidly occupied by a number of free solvent molecules equivalent to the anion volume.
Therefore, other mass variations during the experiment should be due to the free solvent
transfer owing to the formation/creation of free volume inside the film by chain motions
or by accommodation of the charged species in the reactive polymer. Consequently, the
kinetics of this free solvent transfer should be a “fingerprint” to the kinetics of
conformational changes in the films. A priori, this theoretical approach allows both
processes to be decoupled.
A perusal of the literature reveals that very few studies have directly addressed
the kinetics of conformational changes of polymers; partly due to the difficulties reported
about the appropriate techniques available. Recently, Otero and coworkers emphasized
that conformational and structural magnitudes induced by electrochemical reactions are
not included in the chemical kinetic model of ICPs[31,32]. They show an intense
experimental procedure to explore the change of the intermolecular forces during the
electrochemical reactions of polymers. The investigation of the global behavior took into
account all the electrochemical processes involved between the modified electrode and
the solution and the global behavior was explained through structure and thermodynamic
phenomena (structural chemical kinetics).
The motivation of this work is to show a good approximation of the most
physically realistic description of the system where ICP changes its volume to store
inserted ions or solvent molecules by conformational arrangements during the
electrochemical transitions[33–36]. A representative p-type ICP were chosen to test the
applicability of the proposed model to a dynamic molecular system of technological
importance in aqueous media and to explore quantitatively the dynamics of thin films.
Recent works clearly prove that the poly(o-toluidine) (POT) is a good candidate[16,17].
POT is a polyaniline derivative where −CH3 group in the polymer backbone causes
greater electron localization and interchain separation than polyaniline[37]. This fact
favours the formation of two time-stable conducting forms with polarons or bipolarons.
Moreover, literature clearly exhibits their increasing technological interest for this
polymer in electrochromic devices[38], biofuel cell-based devices[39] or biosensors[40].
5
2. Ac-electrogravimetry: Theory and background for anion exclusion in dynamic
polymers
During the redox reaction of a conducting polymer in aqueous or non-aqueous
media, transfer of ionic species can compensate the excess or defect of charge inside a
polymer film, eq (1), the universally accepted concept of coupled electron/ion transfer.
Most conducting polymers ⟨P⟩ lose electrons when the neutral chains are submitted to
anodic potentials generating positive charges with consequent insertion of charge
balancing anions from the solution (p-doping).
Often, the amount of free solvent molecules (not structural) inside a polymeric
matrix is a function of the oxidation state of the polymer to satisfy osmotic and volume
constraints[10]. The insertion of ionic molecules to balance the charge of the oxidized
film involves the displacement of inner solvent molecules. In the simplest situation when
the volume of the holes in the ionic channels remains constant like in rigid polymers, the
amount of, for example, water molecules which can be expelled out from the film during
the anion insertion depends on the volume of anions (Figure 1), therefore, 𝑉A- = 𝑛𝑉H2 O .
In a reverse process, free water molecules from solution can occupy the space left by
anions during the anion expulsion. This fact is known as exclusion[12,30,41].
⟨P, 𝑛H2 O⟩ +
→
A- ←
𝑘e- ,𝑘′A𝑘′e- ,𝑘A-
⟨P+ , A- ⟩ + e- + 𝑛H2 O
(1)
where ⟨P,𝑛H2 O⟩ is the hydrated polymer and ⟨P+ ,A- ⟩ is the polymer matrix doped with
anions A- , 𝑛 being the number of free water molecules excluded during A- insertion. The
parameters, 𝑘A- and 𝑘e- are the kinetic constants of anion and electron expulsion from
polymer, respectively, whereas, the parameters 𝑘A′ - and 𝑘e′- are the kinetic constants of
anion and electron insertion to polymer, respectively.
By assuming that anions transport through very thin films and in electrolytes with
high ionic strength are fast enough, the kinetic constants only depend on the resistance of
anions to cross the polymer|solution interface[42,43]. Then, the kinetic constants of both
electron and anion transfer are equal as follows 𝑘e- = 𝑘A′ - and 𝑘e′- = 𝑘A- .
Gabrielli et al. have extensively described that for very thin polymer films
[22,27,42–45], the change of the concentration of the anions, 𝛥𝐶A- , when a small sine
wave potential perturbation, 𝛥𝐸, is applied as a function of perturbation frequency is:
6
𝛥𝐶A−𝐺A(𝜔) =
𝛥𝐸
𝑗𝜔𝑑𝑓 + 𝐾A-
(2)
where 𝑗 = √−1, 𝜔 is the angular frequency, which equals to 2𝜋𝑓, 𝑓 is the perturbation
frequency, 𝑑𝑓 is the thickness of the polymer film,
𝐾A- = 𝑘A- + 𝑘A′ - 𝐶A𝑠𝑜𝑙
(3)
𝑚𝑎𝑥
′ ′
- ) + 𝑏 - 𝑘 - (𝐶 𝐺A- = −𝑏A- 𝑘A- (𝐶A- − 𝐶A𝑚𝑖𝑛
− 𝐶A- )𝐶A𝑠𝑜𝑙
A A
A
(4)
and
where, 𝐶A- is the concentration of A- in the polymer, 𝐶A𝑚𝑎𝑥
is the maximum concentration
of the sites available for the insertion in the polymer, 𝐶A𝑚𝑖𝑛
is the minimum concentration
of the occupied sites and 𝐶A𝑠𝑜𝑙
is the concentration of species in the solution. The
parameters, 𝑘A- and 𝑘A′ - are the above mentioned kinetic rate constants activated by
potential,
𝑘A- = 𝑘A- 00 𝑒𝑥𝑝(𝑏A- (𝐸 − 𝐸 0′ ))
and
𝑘A′ - = 𝑘A- 00 𝑒𝑥𝑝(𝑏A′ - (𝐸 − 𝐸 0′ )),
respectively where 𝐸 0′ is the formal potential and 𝑘A- 00 is a preexponential factor of the
kinetic rate constants independent of applied potential 𝐸.
The parameters, 𝑏A- and 𝑏A′ - are the Tafel coefficients related to the number of
electrons (𝑛e- ) involved in the faradaic process and the symmetry of direct and reverse
transition with respect to the formal redox potential[46,47]:
𝑏A- − 𝑏A′ - = 𝐵A- =
𝑛e- 𝐹
𝑅𝑇
(5)
where 𝑅 is the gas constant and 𝑇 is the absolute temperature.
In a more sophisticated and realistic model for anion p-doping of ICPs,
electrochemical reactions induce conformational changes such as swelling, shrinking,
compaction or relaxation processes owing to repulsive/attractive interactions inside the
film or formation/destruction of molecular covalent bonds[32]. The reactive film could
act like a molecular pump during a sinusoidal potential perturbation. Accordingly, a
constant thickness of films cannot be considered since it may change depending on the
polarization potential[33–35,48]. Eq (2) can be slightly modified in terms of surface
concentration considering only a bidimensional surface[16,17]:
𝑑𝑓
𝛥𝐶A𝛥ΓA−𝐺A(𝜔) =
(𝜔) =
𝛥𝐸
𝛥𝐸
𝑗𝜔 + 𝐾A′ -
(6)
where 𝐾 ′ = 𝐾 ⁄𝑑𝑓 and, then, 𝑗𝜔𝑑𝑓 changes to 𝑗𝜔.
Based on this model, eq (6) allows the theoretical electrochemical impedance,
𝛥𝐸 ⁄𝛥𝐼(𝜔) to be calculated only for the involved anion transfer. Thus,
7
𝛥𝐸
1
(𝜔) = 𝑅𝑢 +
1
𝛥𝐼
𝑗𝜔𝐶𝑑𝑙 +
𝑍𝑓
(7)
where 𝑅𝑢 is the uncompensated solution resistance, 𝐶𝑑𝑙 is the double layer capacity and
𝑍𝑓 is the faradaic impedance defined as:
1
𝑍𝑓 =
𝑗𝜔𝑆𝐹𝑧A- [
𝐺A]
𝑗𝜔 + 𝐾A′ -
(8)
where 𝑧A- is the valence of the anion, 𝐹 is the Faraday constant, and 𝑆 is the active
electrode surface area. Eq (8) is close to classical Randless equivalent circuit where the
charge transfer resistance and the Warburg element were replaced by a simple 𝑅,𝐶 circuit.
By subtracting the non-faradaic contributions, the electrical charge/potential
transfer function, 𝛥𝑞⁄𝛥𝐸(𝜔), can be calculated as:
𝛥𝑞
1
1
(𝜔) =
− 𝐶𝑑𝑙
𝛥𝐸
𝑗𝜔 𝛥𝐸 (𝜔) − 𝑅
𝑢
𝛥𝐼
(9)
and by using the eq (7) and (6), this theoretical transfer function is equal to:
𝛥𝑞
𝐺A(𝜔) = 𝑆𝐹𝑧A- [
]
𝛥𝐸
𝑗𝜔 + 𝐾A′ -
(10)
Here, non-charged species (free H2 O) do not participate in the charge balance but
the insertion/expulsion of these molecules involves effective mass changes of the reactive
film. Therefore, considering eq (6), the mass/potential transfer function, 𝛥𝑚⁄𝛥𝐸(𝜔), is
easily deduced to:
𝐺H2 O
𝛥𝑚
𝐺A(𝜔) = 𝑆 (𝛿A- 𝑀A- [
])
′ ] + 𝑛𝛿H2 O 𝑀H2 O [
𝛥𝐸
𝑗𝜔 + 𝐾A𝑗𝜔 + 𝐾H′ 2O
(11)
where 𝑀i is the molar mass of the 𝑖 species involved (A- or H2 O) and 𝐾H′ 2O and 𝐺H2 O have
a similar meaning as eq (3) and (4), respectively. The parameter 𝛿A- is +1 due to the
increase of mass when the polymer is oxidized, eq (1). Accordingly, the 𝛿H2O is −1 due
to the decrease of mass resulting from the expulsion of free water molecules induced by
the insertion of anions (exclusion).
In a rigid film, kinetics of free H2 O transfer are governed by kinetics of anion
transfer to satisfy volume constraints (Figure 1)[10]. Consequently, 𝐺A- = 𝐺H2 O and
𝐾A′ - = 𝐾H′ 2O can be easily assumed and, then, eq (11) is simplified to:
𝛥𝑚
𝐺A(𝜔) = 𝑆(𝛿A- 𝑀A- + 𝑛𝛿H2O 𝑀H2O ) [
]
𝛥𝐸
𝑗𝜔 + 𝐾A′ -
(12)
8
In a reactive polymer with a constant thickness in all polarization potentials
considering only the exclusion effect, the capacitive response would show a loop owing
to a single electrochemical transfer (Figure 2a), in this case with charge balancing anions.
On the contrary, the global electrogravimetric response depends on anion mass and anion
volume. As an example, a loop in the first quadrant of the global electrogravimetric
response would appear because the mass of one anion (in this case 80 g mol-1) is higher
than the mass of four (𝑛 = 4) displaced water molecules (in this case 𝑛𝑀H2 O =4·18=72 g
mol-1) due to the anion volume (Figure 2b).
For dynamic polymers, 𝛥𝑞⁄𝛥𝐸(𝜔) has a similar response to the one observed for
rigid polymers. However, electrogravimetric responses, during the same anion transfer,
should depend on the change of film thickness associated to the conformational changes
and the number of H2 O transferred out of exclusion effect (Figure 3). A general
theoretical expression for 𝛥𝑚⁄𝛥𝐸(𝜔) considering both free water transfers from pure
anion exclusion and free water transfer from induced conformational movements can be
expressed as:
𝛥𝑚
𝐺A(𝜔) = 𝑆(𝛿A- 𝑀A- + 𝑛𝛿H2O 𝑀H2O ) [
]
𝛥𝐸
𝑗𝜔 + 𝐾A′ +
𝑆(𝑛′ 𝛿H′ 2O' 𝑀H2O ) [
𝐺H2O'
]
𝑗𝜔 + 𝐾H′ 2O'
(13)
where 𝛿H′ 2O' indicates the direction of transfer and the number of molecules of H2 O
associated with conformational movements (𝑛′ ) can be equal or different than 𝑛. 𝐺H2O'
and 𝐾H′ 2O' are kinetic parameters of free water transfer from induced structural
movements. The method of elimination of the pure anion exclusion from
electrogravimetric results to consider the contribution of other free water transfers is close
to the method used by Bruckenstein and Hillman as a diagnostic for species
interference[5,12,13].
In the situation (a) in Figure 3, the pure exclusion effect can be enhanced due to
the contraction of film (−𝛥𝑑𝑓 ) during the insertion of anions, so, 𝛿H′ 2O' = 𝛿H2O = −1. The
response leads to a net loss of mass during the oxidation of polymer (loop in the third
quadrant of Figure 4)[46]. In the situation (b) of Figure 3, the pure exclusion effect is
balanced due to the expansion of film thickness (+𝛥𝑑𝑓 ). Therefore, 𝛿H′ 2O' = 𝛿H2O = 0,
𝑛 = 𝑛′ = 0 and the electrogravimetric response correspond to a pure anion transfer (loop
in the first quadrant of Figure 4). Finally, a large expansion of film thickness (+2𝛥𝑑𝑓 )
9
creates holes occupied by free H2 O from solution as situation (c) of Figure 3 shows. Here,
𝛿H2O = 0, 𝑛 = 0 and the electrogravimetric response appears in the first quadrant of
Figure 4. Simplistically, the electrogravimetric responses of three situations consider
similar kinetics of anion transfer and conformational changes, 𝐺A- = 𝐺H2 O' and 𝐾A′ - =
𝐾H′ 2O' in eq (13). Thus, if this procedure is assumed, the kinetic constants of free water
molecules experimentally obtained from ac-electrogravimetry, 𝐺H2O' and 𝐾H′ 2O' , could
approximate the kinetics of conformational changes of the polymer.
3. Experimental
3.1. Film preparation
The electrochemical polymer deposition and characterization were performed by
cyclic voltammetry using an AUTOLAB potentiostat-galvanostat (PGSTAT302) and a
lab-made oscillator acted as an Electrochemical Quartz Crystal Microbalance at room
temperature (about 295±2 K). The three-electrode cell involved a reference electrode
(Saturated Calomel Electrode or SCE, Tacussel XR 600) and a platinum counter
electrode. The working electrode was a gold electrode (𝑆 = 0.3 cm2) patterned on a 9
MHz quartz crystal resonator (TEMEX, France). All the solutions were prepared with
deionized and double-distilled water. The potential of the working electrode is referred to
the SCE reference electrode in all measurements.
POT thin films were synthetized for ac-electrogravimetry experiments on a
gold/quartz electrode. The polymerization solution was 0.5 M H2SO4 (Fisher scientific,
for trace analysis) and 0.2 M o-toluidine (Fluka). All chemicals were used as received.
POT was formed through 100 voltammetric cycles between −0.1 V and 0.9 V at 100 mV
s-1 scan rate (which equals to ~ 40 µg cm-2 deposited film mass). The films generated
following this procedure show a more open structure owing to the properties of bisulfate
anions[49,50].
3.2. Film conditioning
POT film was 10 times cycled between -0.1 V and 0.9 V in 0.5 M H2SO4 at 100
mV s-1 until a stable cyclic voltammogram was obtained avoiding significant polymer
degradation by hydrolysis[17]. Afterwards, ac-electrogravimetry studies were performed
at steady-state potentials in the range of 0.55 V to 0.1 V in the same solution.
3.3. ac-Electrogravimetry set-up
For ac-electrogravimetry studies, a fast quartz crystal microbalance was coupled
with a four-channel frequency response analyzer (FRA, Solartron 1254) and a potentiostat
10
(SOTELEM-PGSTAT Z1). The modified working electrode was polarized at a given
potential and a sinusoidal potential perturbation with a small amplitude (10 mV rms) was
superimposed between 65 kHz and 0.01 Hz. The microbalance frequency change, 𝛥𝑓𝑚
and the alternating current response, 𝛥𝐼, were sent to the four channels FRA, which
allowed the electrogravimetric transfer function, 𝛥𝑚⁄𝛥𝐸(𝜔) and the electrochemical
impedance, 𝛥𝐸 ⁄𝛥𝐼(𝜔), to be simultaneously obtained. Finally, the experimental data
were fitted with the theoretical expressions given in Section 2 by means of LevenbergMarquardt method[51].
4. Results and discussion
4.1. Kinetic model for POT films in acidic aqueous media
In acidic solutions, the voltammetric response of POT films has two successive
quasi-reversible redox process independent from the existing anion (inset of Figure
5a)[52–54]. In the oxidation direction, the first redox process involves the transfer of
anions (A- ) to keep the electroneutrality during the leucoemeraldine-polaron (LE⇄P)
transitions. The second redox process corresponds to bipolaron-pernigraniline transitions
(BP⇄PN) with the transfer of H3 O+ which is necessary for protonation/deprotonation of
electroactive sites.
By cyclic spectro-electrogravimetry and ac-electrogravimetry[16,53], a third
reaction step was elucidated corresponding to the polaron-bipolaron (P⇄BP) transitions
with specific and independently measurable electrochemical properties. The
electrochemical mechanism can be summarized as:
LE +
P+
A- →←
A- →←
BP←→
𝑘′1
𝑘1
𝑘′2
𝑘2
𝑘3
𝑘′3
P + e- + 𝑥1 H2 O
(14)
BP + e- + 𝑥2 H2 O
(15)
PN + e- + H3 O+
(16)
where 𝑥𝑖 represents the net effective number of water molecules exchanged during the
electrochemical transition and depends on the nature of the anion transferred[17].
Moreover, the electrochemical transitions of eq (14) and (15) are kinetically faster than
the electrochemical transitions of eq (16).
Accordingly, LE⇄P (eq (14)) and P⇄BP (eq (15)) transitions are good candidates
to test the anion exclusion model for dynamic polymers. Thus, ac-electrogravimetric
experiments were carried out in the potential range of 0.55 V to 0.1 V in 0.5 M H2SO4
11
acid solution. In the potential range of 0.45 and 0.1 V, LE⇄P and P⇄BP transitions are
expected as it was described elsewhere[53]. The experimental charge/potential transfer
function results represented in a complex capacitance plane, 𝛥𝑞⁄𝛥𝐸(𝜔), show a typical
loop at 0.25 V associated to one charge transfer balanced by HSO-4 (Figure 5a). Around
0.45 V, the partial charge transfer associated with the H3 O+ transfer must be taken into
account and be separated. Moreover, the quasi-vertical branch observed at low
frequencies and at potentials close to 0.1 V points to a slight contribution of a parasitic
reaction which can be removed using a simple 𝑅𝑝 , 𝐶𝑝 circuit.
In accordance with previous works[16], the theoretical equation of 𝛥𝑞⁄𝛥𝐸(𝜔) for
POT films in 0.5 M H2SO4 acid solution can be proposed from eq (10) considering
𝑧HSO-4 = 𝑧H3 O+ = 1 as:
𝐹𝐺HSO-4
𝐹𝐺H3 O+
𝛥𝑞
1
(𝜔) =
+
+
𝛼
𝛼
′
1 (𝑗𝜔) HSO4 + 𝐾HSO
𝛥𝐸
(𝑗𝜔) H3O+ + 𝐾H′ 3 O+
𝑗𝜔𝑅𝑝 +
4
𝐶𝑝
(17)
The non-ideality of impedance spectra (deviation from a perfect semicircle) can
be mathematically corrected using a constant-phase element, (𝑗𝜔)𝛼 . This fact is
frequently observed in intercalation systems[55,56]. Here, (𝑗𝜔)𝛼 is considered as a
mathematical resource to achieve the best fittings and it does not cause any change in the
physical meaning of the kinetic parameters[16].
Eq (17) was fitted to experimental 𝛥𝑞⁄𝛥𝐸(𝜔) until convergence to obtain
valuable kinetic information of both ions transfers. Solid line Figure 5a shows a good
agreement between the experimental and simulation data using eq (17). Later, 𝐺HSO-4 ,
′ 𝐾HSO
, 𝛼HSO-4 , 𝐺H3 O+ , 𝐾H′ 3 O+ and 𝛼H3 O+ parameters are used for subsequent
4
electrogravimetric analysis. 𝛼HSO-4 and 𝛼H3 O+ obtained are close to the ideal system for
both involved species (0.94±0.04).
Figure 5b shows the corresponding electrogravimetric response of POT film at
0.25 V. A single loop in the first quadrant indicates the increase of mass during the
oxidation. Therefore, insertion of anions is expected to balance charge excess. For the
multiparametric fitting process, eq (13) was used with similar modification as it is
commented above in section 2. At more anodic potentials, the partial contribution to
𝛥𝑚⁄𝛥𝐸(𝜔) associated with H3 O+ transfer was added. Finally, a general theoretical
equation of 𝛥𝑚⁄𝛥𝐸(𝜔) for POT films in 0.5 M H2SO4 acid solution considering the
12
anion exclusion, free water transfer out of exclusion effect and H3 O+ transfer can be
defined as:
𝐺HSO-4
𝛥𝑚
(𝜔) = (𝛿HSO-4 𝑀HSO-4 + 𝑛𝛿H2O 𝑀H2 O ) [
]
𝛼HSO4 + 𝐾′
𝛥𝐸
(𝑗𝜔)
HSO4
′
+ (𝛿H′ 2O' 𝑀H2O ) [
𝑛 𝐺H2O'
]
𝛼H2 O'
(𝑗𝜔)
+ 𝐾H′ 2O'
+ (𝛿H3 O+ 𝑀H3 O+ ) [
𝐺H3 O+
𝛼H O+
(𝑗𝜔) 3 +
𝐾H′ 3 O+
(18)
]
In the present form, this function is over-parameterized. For this reason, to reduce
the number of parameters, some of them were fixed. Thus, 𝛿HSO-4 𝑀HSO-4 is +97 g mol-1,
′ 𝛿H2O 𝑀H2 O = −18 g mol-1 and 𝛿H3 O+ 𝑀H3 O+ = −19 g mol-1. The parameters 𝐺HSO-4 , 𝐾HSO
,
4
𝛼HSO-4 , 𝐺H3 O+ , 𝐾H′ 3 O+ and 𝛼H3 O+ are fixed from results of fitted Δ𝑞 ⁄Δ𝐸(𝜔) function at a
given polarization potential. The parameter 𝑛 was calculated considering 𝑉HSO-4 = 47 Å3
and 𝑉H2 O = 10 Å3 obtained from the Connolly Solvent Excluded Volume in the
commercial software ChemBio3D Ultra v. 12.0 ChemBioOffice 2010, thus 𝑛 = 4.7.
Initially, 𝛿H′ 2O' 𝑀H2 O could be +18 g mol-1 or −18 g mol-1 because the conformational
changes of film are unpredictable. For this reason, both values were used to perform the
fittings. The better convergence between the experimental and theoretical values were
obtained using 𝛿H′ 2O' 𝑀H2O =+18 g mol-1 and, for this reason, this parameter was fixed as
such (solid line in Figure 5b). Finally, only three parameters (𝑛′ 𝐺H2 O' , 𝛼H2O' and 𝐾H′ 2 O' )
are kept free during multiparametric fittings. Like above, 𝛼H2 O' obtained is close to the
ideality at all polarization potentials (0.95±0.02).
Determination of 𝒏′ . At this point, eq (17) and (18) can explain properly the
electrochemical behavior of POT films, as shown by the fits obtained (solid lines in Figure
5). However, 𝑛′ is still an unknown parameter and an apparent 𝑛′ 𝐺H2O' was obtained. In
this form, 𝑛′ 𝐺H2O' cannot provide a valuable information on the conformational kinetics
of the film but it may be refined.
As it was mentioned in section 2, 𝑛′ represents the number of water molecules
transferred by changes of free volume inside the films owing to conformational changes
during the electrochemical reactions. By taking into account the schemes provided in
Figure 3, one electron transfer involves one monovalent anion transfer, the transfer of one
13
set of water molecules owing to exclusion effect (𝑛H2 O) and the transfer of one set of
water molecules out of exclusion effect (𝑛′ H2 O).
In terms of surface concentration, since the thickness of film is changing, the
surface concentration of transferred anions would be equal to the surface concentration
of transferred 𝑛H2 O and transferred 𝑛′ H2 O, 𝛤HSO-4 = 𝛤H2 O = 𝛤H2 O' . Taking this into
account, the stoichiometric relation between anions and H2 O' (𝑛′ ) can be estimated from
the derivative of the surface insertion law with respect to the potential at 𝜔 = 0, 𝑑𝛤𝑖 ⁄𝑑𝐸
(eq (6)) as[16,17]:
′ 𝑛′ 𝐺H2 O' 𝐾HSO
𝑑𝛤H2 O'
𝑑𝐸
4
= 𝑛′
|
|
′
𝐾H2 O' 𝐺HSO-4
𝑑𝐸 𝜔⟶0 𝑑𝛤HSO-4
= 𝑛′
𝜔⟶0
𝑑𝛤H2 O'
|
𝑑𝛤HSO-4
= 𝑛′
(19)
𝜔⟶0
Figure 6 shows the number of water molecules excluded per anion transfer, 𝑛, as
a reference and the number of transferred water molecules owing to the conformational
changes of film during the electrochemical reaction of POT, 𝑛′ , calculated from eq (19)
between 0.45 V and 0.1 V. As it was commented above, 𝑛 is a constant parameter at all
polarization potentials (4.7), however, 𝑛′ , changes between 1 and 2 water molecules
owing to the conformational changes of film with a maximum around 0.25 V. This means
that the free volume inside the film where H2 O can be inserted owing to conformational
changes depends on the oxidation state of film induced by the applied potential, or in
other words, it depends on film structure and the amount of anions inside the film. As an
example, the film is more oxidized (BP form) and anion doped at 0.45 V than at 0.1 V
where POT is more reduced (LE form) and undoped of anions (Table 1).
Once 𝑛′ was obtained, 𝐺H2O' can be calculated for a set of water molecules
transferred during the conformational changes. Later, this parameter together with 𝐾H′ 2 O'
will be used to evaluate the kinetics of conformational changes of POT films under the
experimental conditions in this work.
Identification of electrochemical processes. Before going into the detailed
analysis of the kinetic parameters, the electrochemical transitions of POT can be placed
on the potential scale by means of the derivative of the surface insertion laws of 𝐻𝑆𝑂4− ,
′ 𝑑𝛤HSO-4 (𝐸)⁄𝑑𝐸 = 𝐺HSO-4 ⁄𝐾HSO
[16]. The peaks in Figure 7 have the same meaning as the
4
theoretical derivation of a voltammetric response of electrochemical processes and, in
this case, they correspond to LE⇄P and P⇄BP transitions where the anion transfer takes
place. The experimental result were fitted to [16,27,57]:
14
𝑑𝛤HSO-4
𝑑𝐸
|
=
𝑑𝛤HSO-4
𝑒𝑥𝑝
𝑑𝐸
|
+
𝑑𝛤HSO-4
𝐿𝐸⇄𝑃
𝑑𝐸
|
(20)
𝑃⇄𝐵𝑃
where for each reaction
𝑑𝛤HSO-4
𝑑𝐸
𝐵HSO-4
=
4
∆𝛤HSO-4
𝑐𝑜𝑠ℎ2 [
𝐵HSO-4
(𝐸 − 𝐸𝑝,HSO-4 )]
2
(21)
𝑚𝑎𝑥
𝑚𝑖𝑛
- −𝛤
and ∆𝛤HSO-4 = 𝛤HSO
HSO-4 is the increment between the minimum surface concentration
4
𝑚𝑖𝑛of the sites occupied by anions in the polymer (𝛤HSO
) and the maximum surface
4
𝑚𝑎𝑥
- ) during the redox
concentration of the sites available for anion insertion (𝛤HSO
4
conversion, and 𝐸𝑝,HSO-4 is the peak potential where 𝑑𝛤(𝐸)⁄𝑑𝐸 is higher. Therefore,
valuable information about 𝐵HSO-4 , ∆𝛤HSO-4 and 𝐸𝑝,HSO-4 can be obtained for each transition
process[54].
The peak at 0.124 V corresponds to LE⇄P and the peak at 0.384 V to the P⇄BP.
About two LE⇄P (28 nmol cm-2) per one P⇄BP (14 nmol cm-2) occur in the POT film
during the potential scan. This difference could be due to two possible formation of
bipolaronic forms (BP) inside the film: i) electrochemically by oxidation of an
electroactive site next to a formed polaron (eq (22)) or ii) by electronic reconfiguration
from two electrochemically formed polarons (eq (23))[58,59]:
H
H
CH3
+
CH3
H
-e-, +HSO4-
N
N
-
CH3
+
N
H
N
O
H
CH3
+e-, -HSO4-
S O
H
H
CH3
H
CH3
H
H
H
-
O
S O
CH3
O
S O
H
CH3
H
O
CH3
N
O S O
O
+
(23)
O
H
H
(22)
N
N
O
O
CH3
+
N
-
O
S O
N
CH3
H
O
-
N
CH3
N
O
O
H
CH3
+
+
CH3
N
N
N
H
N
O
O S O
O
+
O
O
H
H
N
CH3
H
H
CH3
Consequently, the electronic reconfiguration in POT would reduce the amount of
BP, which can be formed electrochemically by a superimposed potential.
Ease of species transfer at the polymer|solution interface. From an electrical
point of view[60], kinetic parameters, 𝐺𝑖 , are analog to the inverse of a charge transfer
resistance at the polymer|solution interface, 1⁄𝐹𝐺 = 𝑅𝑐𝑡 . Therefore, it refers to the ease
of species transfer during the electrochemical reactions of electroactive films.
For anions and H2 O′ transfers, two peaks of 𝐺𝑖 are expected because both species
are involved in two different electrochemical processes, LE⇄P and P⇄BP. However,
anions and solvent transfers show only one peak of 𝐺𝑖 in Figure 8 centered at ~ 0.32 V
15
where both transitions take place simultaneously (see Figure 7). This particular behavior
was previously explained considering that one specie (anion or water) can be inserted in
two structurally different sites of the film (P or BP sites)[16].
The exponential dependence at potentials far from the peak potential agrees with
the proposed model[61]:
𝐺𝑖 =
𝐺𝑖𝑚𝑎𝑥
𝐵
𝑐𝑜𝑠ℎ [ 𝑖 (𝐸 − 𝐸𝑝,𝑖 )]
2
(24)
where 𝑖 is HSO-4 or H2 O', 𝐺𝑖𝑚𝑎𝑥 represents the maximum value for this function at 𝐸= 𝐸𝑝,𝑖 ,
and 𝐸𝑝,𝑖 represent the peak potential of 𝐺𝑖 .
By taking into account eq (5), for the direct transitions (oxidation half-reactions):
𝐵𝑖 𝑛e- 𝛼𝐹
=
2
𝑅𝑇
(25)
and for the reverse transitions (reduction half-reactions):
𝐵𝑖 𝑛e- (1 − 𝛼)𝐹
=
2
𝑅𝑇
(26)
are obtained. Values of 𝛼=0.5 imply that the variation of 𝐺𝑖 on the applied potential
presents a symmetry with respect to the formal redox potential, and values for 𝐵𝑖 are the
same for the direct and reverse transitions. In any other case, 𝐵𝑖 values are different, and
the dependence of 𝐺𝑖 on the applied potential should be asymmetrical.
At 298 K, 𝐵𝑖 ⁄2 = 39 V-1 for 𝑛e- =2 and 𝛼=0.5, one electron for LE⇄P transitions
which takes place mainly between 0.1 and 0.32 V and one electron for P⇄BP transitions
which takes place mainly between 0.35 V and 0.55 V[17]. Thus, it is possible to obtain
an estimation of this parameter for the reverse and forward reactions from the slope of
log(𝐺H2 O' ) versus 𝐸 plot (Figure 8).
Values obtained for the different slopes are close to 39 V-1 for HSO-4 and H2 O' as
expected theoretically. Therefore, about 20 V-1 correspond to each of the transitions.
These results are in agreement with the 𝐵𝐻𝑆𝑂4− values obtained from fittings of
𝑑ΓHSO-4 (𝐸)⁄𝑑𝐸 in Figure 7 where 𝐵HSO-4 for LE⇄P is 13 V-1 and 𝐵HSO-4 for P⇄BP is 18 V1
.
Previous studies of POT films immersed in different acids show relatively lower
values as the anion interacts more strongly with films[17]. Lateral interactions between
randomly distributed electroactive sites during the electrochemical reaction of films
reduce the theoretical value of 𝐵𝑖 considering the Laviron model deduced from
16
thermodynamic basis of the Frumkin-type isotherm[62]. Therefore, lateral interactions
are more likely to occur during LE⇄P than during P⇄BP. This fact can be due to the
extent of doping in the film, see Table 1. Higher amount of anions inside the film (as it
occurs during P⇄BP) can separate the molecular chains by repulsion, as a result reduces
the strength of lateral interactions. On the contrary, stronger lateral interaction can be
expected at lower doped states of polymer as at potentials where LE⇄P takes place,
reducing the distance between charged electroactive sites (inter-chain or intra-chain).
The evolution of 𝐺HSO-4 and 𝐺H2 O' with respect to the potential is very similar;
therefore, they show a similar ease to cross the polymer|solution interface. This fact
agrees with the proposed model, which assumes that non-charged species transfer can be
kinetically controlled by charge injection in polymeric backbone to induce
conformational changes. At 0.32 V, the formation of the polaronic structure of POT films
which twists the structure (coil structures owing to the anion-POT interactions) results in
more water molecules that are able to be ejected from the film owing to conformational
changes (𝑛′ close to 2 in Figure 6)[63,64]. Indirectly, this agrees with the
expansion/contraction of film owing to the single/double bond transitions and to the
accommodation of anions inside the film.
Rate of species transfer at the polymer|solution interface. In general, the most
important feature is that all transfer processes could be kinetically controlled by injected
charge in the polymer, in other words, it can be modulated depending on the applied
potential. Figure 9 shows 𝐾H′ 2 O' and 𝐾A′ - values obtained by fittings. Although similar rates
are reached for both species, interestingly some differences were found completing
mechanistic details of POT electrochemistry. Between 0.1 and 0.3 V where mainly LE⇄P
takes place, the conformational changes of film allows a set of water molecules to be
transferred faster than anions. The lower amount of anions inside the films could be the
cause for this. On the contrary, the exclusion effect caused by anions is faster than the
conformational changes when POT film is doped with anions. This takes place between
0.3 and 0.45 V where mainly P⇄BP occurs.
The maximum of transfer rate takes place in both species around 0.32 V, as it is
the case in Figure 8. As above, the creation of polaronic forms is a serious structural
perturbation which can involve conformational movements of the molecular chains
making the non-charged species transfer faster[63,64].
17
5. CONCLUSIONS
ac-Electrogravimetry has been used to explore the mechanistic aspects of
electroactive POT thin films. A new electrogravimetric model is proposed which takes
into account the exclusion of free water molecules by anions. Any other
electrogravimetric response of the films can be related to the free water transfer owing to
conformational movements of electroactive and dynamic film. Consequently, the kinetic
aspects studied by ac-electrogravimetry of this kind of free water molecules act as a
“fingerprint” of the kinetic aspects of polymeric movements. Here, the experimentally
accessible timescale allows temporal resolution of coupled electron/anion transfer/free
solvent transfer and coupled free solvent transfer/polymer structural reconfiguration.
This model was applied to an intensively studied polymer with anion dopingdedoping with interesting results, specifically to POT. The experimentally accessible
timescale allows temporal resolution of species transfer and polymer reconfigurations to
be determined. For this film, the kinetics of conformational changes depends on the
electrochemical reaction. Slightly faster free water transfers/conformational than anion
insertion is observed during LE⇄P transitions. On the contrary, faster anion exclusion
takes place during P⇄BP transitions. This fact has been related to the doped state of
polymer and lateral interactions between electroactive sites. A more open structure of
POT allows faster anion transfers than that in the case caused by the molecular
rearrangements during P⇄BP transitions. This fact is due to the high doping levels in
POT, which reduces the strength of lateral interactions. However, faster macromolecular
movements are necessary before anion transfer owing to the packed state of POT during
LE⇄P transitions. The packed state of POT is driven by a lower doping level involving
stronger interactions.
Although this work focuses on p-type ICPs, the proposed model provides a
platform to extend the mechanistic interpretation of any type of ICPs by impedance
techniques where solvent transfer and polymer reconfigurations follow the charge transfer
steps. Using this model, they can be temporally separated, to the best of our knowledge,
in an unprecedented detail. Therefore, it suggests that there is a considerable volume of
under-exploited materials and experimental conditions further available for this kind of a
study.
18
ACKNOWLEDGMENTS
Part of this work was supported by FEDER-CICyT project CTQ201128973/BQU.
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23
TABLES
Table 1. Variation of the global insertion law by integration of the simulated partial curves
of 𝑑𝛤HSO-4 ⁄𝑑𝐸 of POT film in 0.5 M H2SO4 aqueous solution of Figure 7. Total 𝛤HSO-4 and
𝛤HSO-4 of LE⇄P and P⇄BP transitions are calculated.
𝐸/V
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Total
LE⇄P
P⇄BP
-2
𝛤HSO-4 / nmol cm
0
0
0
4.6
0.1
4.7
8.7
0.4
9.1
11.8
1.0
12.8
13.8
2.4
16.2
14.9
4.8
19.7
15.6
7.8
23.4
15.9
10.6
26.5
24
FIGURES CAPTIONS
Figure 1. Scheme of the electrode|polymer|solution electrode during p-doping of a rigid
polymer by anions (A- ) considering the exclusion of free water molecules (H2 O). 𝑑𝑓 is
the polymer film thickness. 𝑘A- and 𝑘e- are the kinetic constants of anion and electron
expulsion from polymer, respectively. 𝑘A′ - and 𝑘e′- are the kinetic constants of anion and
electron insertion to polymer, respectively. The circles represent the molecule volume. In
this case, 𝑉A- = 4𝑉H2O . The different color of water molecules allows the water inside
film and water in solution to be distinguished.
Figure 2. Simulation in the complex plane of 𝛥𝑞⁄𝛥𝐸(𝜔) (a) and 𝛥𝑚⁄𝛥𝐸(𝜔) (b)
considering a pure exclusion of effect like in Figure 1 between 40 KHz and 1 mHz of
frequency perturbation. The parameters used in eq (10) and (12) are 𝐺A- = 1x10−5 mol
cm-2 V-1, 𝐾A′ - = 70 s-1, 𝑧A- = 1, 𝑆 = 0.3 cm2, 𝛿A- 𝑀A- = +80 g mol-1, 𝛿H2O 𝑀H2O = −18
g mol-1. 𝑛 = 4, therefore the volume of one anion exclude 4 water molecules (𝑉A- =
4𝑉H2 O ). Black squares are global ac-electrogravimetric response, red circles are the partial
ac-electrogravimetric response of anion and blue triangles are the partial acelectrogravimetric response of free H2 O.
Figure 3. Scheme of the electrode|polymer|solution electrode during p-doping of a
polymer by anions (A- ) considering the contraction of polymer (a), the expansion of
polymer (b) and (c) together with the transfer of water molecules. 𝑘A- and 𝑘e- are the
kinetic constants of anion and electron expulsion from polymer, respectively. 𝑘A′ - and 𝑘e′are the kinetic constants of anion and electron insertion to polymer, respectively. ∆𝑑𝑓 is
the film thickness increment. The different color of water molecules allows H2 O from
film and solution to be distinguished.
Figure 4. Simulation in the complex plane of 𝛥𝑚⁄𝛥𝐸(𝜔) considering the exclusion of
effect between 40 KHz and 1 mHz of frequency perturbation together with changes of
polymer thickness like in Figure 3. The parameters used in eq (13) are 𝐺A- = 𝐺H2 O' =
1x10−5 mol cm-2 V-1, 𝐾A′ - = 𝐾H′ 2 O' = 70 s-1, 𝑧A- = 1, 𝑆 = 0.3 cm2, 𝛿A- 𝑀A- = +80 g mol1
and 𝑀H2O = 18 g mol-1. In situation (a), 𝛿H′ 2O' = 𝛿H2O = −1 and 𝑛 = 𝑛′ = 4. In
25
situation (b), 𝛿H′ 2O' = 𝛿H2O = 0 and 𝑛 = 𝑛′ = 0. In situation (c), 𝛿H′ 2O' = 1, 𝑛′ = 4,
𝛿H2O = 0 and 𝑛 = 0.
Figure 5. Experimental and theoretical charge/potential transfer function, 𝛥𝑞⁄𝛥𝐸(𝜔) (a),
and mass/potential transfer function, 𝛥𝑚⁄𝛥𝐸(𝜔) (b), of POT film in 0.5 M H2SO4
aqueous solution at 0.25 V. Cyclic voltammetry of a POT film between -0.1 V and 0.9 V
at 100 mV s-1 in the same solution in the inset of (a).
Figure 6. Number of water molecules (H2 O) excluded per anion transfer, 𝑛, and number
of transferred water molecules (H2 O') owing to conformational changes, 𝑛′ , calculated
from eq (19) between 0.45 V and 0.1 V of POT film in 0.5 M H2SO4 aqueous solution.
Figure 7. Evolution of the derivative of the insertion law of HSO-4 , 𝑑𝛤HSO-4 ⁄𝑑𝐸 , at different
polarization potentials of POT film in 0.5 M H2SO4 aqueous solution. Solid lines are
simulations with eq (20) and (21) using the reached parameters by fitting of experimental
results (red circles) where LE⇄P and P⇄BP transitions can be separated. The parameters
are included inside the plot for each transition.
Figure 8. 𝐺HSO-4 and 𝐺H2 O' evolution with respect to potentials perturbation obtained by
fitting 𝛥𝑞⁄𝛥𝐸(𝜔) and 𝛥𝑚⁄𝛥𝐸(𝜔) of POT film in 0.5 M H2SO4 aqueous solution.
′ Figure 9. Rate transfer of exclusion effect represented with values of 𝐾HSO
and rate
4
transfer of conformational changes represented with the values of 𝐾H′ 2 O' at different
polarization potentials obtained by fitting 𝛥𝑞⁄𝛥𝐸(𝜔) and 𝛥𝑚⁄𝛥𝐸(𝜔) with the
theoretical functions of POT film in 0.5 M H2SO4 aqueous solution.
26
FIGURES
Electrode
Polymer
Solution
ionic channel
H2O
H2O
H2O
k'e
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
kA
k'A
H2O
H2O
H2O
Solution
ionic channel
H2O
H2O
H2O
Polymer
H2O
H2O
H2O
Electrode
H2O
H2O
H2O
H2O
H2O
-
AH2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
kA
H2O
-
H2O
-
H2O
k'e
-
H2O
H2O
A
-
H2O
H2O
H2O
k'A
-
H2O
H2O
-
H2O
+
e-
H2O
ke
-
df
H2O
+
eke
-
H2O
H2O
df
Figure 1
27
a
-Im(q/E) / mC cm-2 V-1
4
3
2
1
1 mHz
40 KHz
0
0
1
2
3
4
Re(q/E) / mC cm-2 V-1
Figure 2a
28
4
(m/E)
(m/E)A
-Im(m/E) / g cm-2 V-1
3
b
-
(m/E)H O
2
2
1
1 mHz
0
40 KHz
1 mHz
1 mHz
-1
-2
-3
-4
-4
-3
-2
-1
0
1
2
3
4
Re(m/E) / g cm-2 V-1
Figure 2b
29
Electrode
Polymer
a)
Solution
ionic channel
H2O
H2O
H2O
k'e
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
kA
k'A
H2O
H2O
H2O
Solution
ionic channel
H2O
H2O
H2O
Polymer
H2O
H2O
H2O
Electrode
H2O
H2O
AH2O
H2O
k'e
-
H2O
H2O
H2O
H2O
H2O
kA
H2O
A-
-
H2O
H2O
H2O
H2O
H2O
-
H2O
H2O
H2O
k'A
H2O
-
H2O
H2O
H2O
-
e
+
eH2O
ke
-
H2O
ke
H2O
-
H2O
df-df
df
b)
H2O
H2O
-
H2O
+
-
c)
Electrode
Polymer
ionic channel
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
k
'
e-
H2O
H2O
H2O
H2O
H2O
H2O
k'A
H2O
-
-
df+df
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
k
H2O
ke
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
H2O
'
e-
H2O
H2O
H2O
H2O
H2O
H2O
H2O
kA
k'A
H2O
-
-
H2O
H2O
+
e-
H2O
H2O
H2O
A-
+
e-
H2O
H2O
kA
Solution
ionic channel
H2O
H2O
AH2O
Polymer
H2O
H2O
H2O
H2O
Electrode
Solution
H2O
ke
-
df+2df
Figure 3
30
situation a
situation b
situation c
6
-Im(m/E) / g cm-2 V-1
4
2
1 mHz
0
40 KHz
1 mHz
1 mHz
-2
-4
-6
-6
-4
-2
0
2
4
6
Re(m/E) / g cm-2 V-1
Figure 4
31
8
a
4
0
-Im(q/E) / mC cm-2 V-1
-2
-2
/ mA cmcm
j / jmA
2
6
-2
-4
-6
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
E vs SCE / V
E vs SCE / V
4
10 Hz
2
0.01 Hz
1 Hz
100 Hz
0.1 Hz
0
0
2
4
6
8
Re(q/E) / mC cm-2 V-1
Figure 5a
32
4
b
-Im(m/E) / g cm-2 V-1
3
2
10 Hz
1
1 Hz
0
0.01 Hz 0.1 Hz
100 Hz
0
1
2
3
4
Re(m/E) / g cm-2 V-1
Figure 5b
33
6
number of free H2O
5
n
4
3
2
n'
1
0.1
0.2
0.3
0.4
0.5
E vs SCE / V
Figure 6
34
75
leucoemeraldine-polaron
transition
50
polaron-bipolaron
transition
4
d/dEHSO / nmol cm-2 V-1
100
25
 = 28 nmol cm-2
 = 14 nmol cm-2
B = 13 V-1
Ep = 0.124 V
B = 18 V-1
Ep = 0.384 V
0
0.1
0.2
0.3
0.4
E vs SCE / V
Figure 7
35
42 V-1
1
39 V-1
4
GHSO / mol s-1 cm-2 V-1
10
0.1
2
GH O' / mol s-1 cm-2 V-1
10
35 V-1
1
40 V-1
0.1
0.1
0.2
0.3
0.4
0.5
E vs SCE / V
Figure 8
36
4
K'HSO / s-1
60
60
50
50
40
40
30
30
20
20
10
10
0
0
2
70
KH' O' / s-1
70
0.1
0.2
0.3
0.4
0.5
E vs SCE / V
Figure 9
37